Alexandria city officials, faced with a legislative deadline to fix its outdated combined sewers that engineers suggest is too aggressive, are appealing to Gov. Terry McAuliffe to give them a few more years to replace the system that spills runoff and sewage into the Potomac River during rainstorms.

The General Assembly this week stood by its order that Alexandria fix the problem by 2025, rejecting an amendment from McAuliffe to provide the city three to five additional years to complete the massive infrastructure project. McAuliffe (D) now has the option of letting that bill become law or vetoing it.

Virtually every time it rains, the 200-year-old sewers that serve a portion of Old Town are overwhelmed. Instead of sending the sewage and runoff to the local wastewater treatment plant, the four major sewer “outfalls” dump millions of gallons of effluent per year into the Potomac and its tributaries.

Fixing this requires not just new pipes but also the construction of several football-field-size holding tanks deep beneath the highly populated streets and parks of Old Town. City officials estimate the cost of the project at $386 million over the next 10 years, to be paid for primarily by local property owners.

While the proposed sewer tax increase of more than 500 percent by 2027 may be hard to swallow, especially for the less well-off residents of this expensive suburb, city officials said their objections to the legislative action was never about money, only about the pace of the project.

Mayor Allison Silberberg (D) said the city has taken major steps since May to address the decades-old problem, including action in November to speed up by 14 years its response to a portion of the problem. City leaders “got the message” this winter that legislators and the public want faster solutions, she said.

“We are fully committed to working with all deliberate speed to getting all four outfalls in Alexandria done and to getting them done right,” said Silberberg, who describes herself as a lifelong environmentalist. “This issue has been festering for years and even decades. We are committed to moving forward swiftly.”

But the General Assembly’s deadlines are unrealistic, given the work that must be done, city engineers have told her. The city’s transportation and environmental services director told The Washington Post in January that Alexandria “is being asked to do something in 7½ years that normally takes other communities a generation.”

A gubernatorial veto, Silberberg said, will not slow the city’s work to replace the outdated sewer systems.

State Sen. Adam P. Ebbin (D-Alexandria), who led the fight in Richmond on behalf of the city, said that even if McAuliffe vetoes the legislation, he thinks the issue may re-emerge next year.

“I am hopeful that a workable time frame could be agreed to,” he said. “The city will be expeditiously addressing the problem, and if there are circumstances beyond their control, I will seek extra time.”